The "K" is a misprint. The son's name is given in full on CheshireBMD website as Robert Henry SWAIN, mother DREW, born Birkenhead.

Without knowing his date of birth, it is not easy to find what happened to Robert Laurence/Lawrence SWAIN. I can't see anyone with that full name or similar. There is a Robert SWAIN born 6 November 1878, baptised 19May1887 at St Anne's birkenhead, parents William and Agnes. Death of Robert SWAIN age 76 June 1955 Birkenhead vol 10a p12. You would need to get his marriage certificate to confirm his father. The birth certificates for Minnie's children may show if they were adopted, although legal adoption did not start until the late 1920s, so they might be too early. Aso, if they were adopted, there is no clue given to their new name or adoptive parents.